I tried the game out, beat all the introduction levels and a couple of the challenge one.
I like the game idea and have been following your posts in the /agdg/ threads, this was one of the first games I wanted to try out!
The game was fairly easy to understand in the introduction levels and I had a sense of what was going on while playing them, but the challenge levels made me feel lost really quickly. Maybe it was just the difficulty spike being brutal, but I had no idea when I was advancing in a puzzle. There is no sense of "this is the correct move" until all moves are spent. Some kind of lead or way to know real progress is being made would be welcome.
On the same note, it is too hard to know how a single move will affect the board. You aren't just telling cats where to move, but what will they do when they arrive and how they will retreat to their old place if they break something. And you are not moving one, but sometimes all of the cats in the entire level with just a single move! This results in a playstyle which is more poke the playfield and see what happens rather than picturing the reaction in your head.
I understand why you need cats to be confused when they have 2 or more possible moves, but at the moment it makes the game feel unresponsive.
I really like puzzle games and this one has a lot of potential, so I hope the advice you get here will be helpful for you and your game. Good luck!